WO2001095503A1

WO2001095503A1 - Method and apparatus for enhanced forward error correction in a network

Info

Publication number: WO2001095503A1
Application number: PCT/US2001/017484
Authority: WO
Inventors: Nandakumar Ramanujam; Howard Kidorf; Andrej Puc; Franklin Kerfoot
Original assignee: Tycom (Us) Inc.
Priority date: 2000-06-05
Filing date: 2001-05-31
Publication date: 2001-12-13
Also published as: US20020056064A1; US6622277B1; AU2001271278A1

Abstract

A method and apparatus to perform error correction is described. A stream of data is encoded using concatenated error correcting codes. The encoded data is communicated over a long-haul transmission system. The encoded data is decoded using the codes.

Description

METHOD AND APPARATUS FOR ENHANCED FORWARD ERROR CORRECTION IN A NETWORK

FIELD OF THE INVENTION

The invention relates to communications networks in general. More particularly, the invention relates to a method and apparatus for enhancing forward error correction in a network such as a long-haul communications network.

BACKGROUND OF THE INVENTION

The capacity of long-haul communication systems, such as "undersea" or

"submarine" systems, has been increasing at a substantial rate. For example, some long-haul optically amplified undersea communication systems are capable of transferring information at speeds of 10 gigabits per second (Gbps) or greater. Long-haul communication systems, however, are particularly susceptible to noise and pulse distortion given the relatively long distances over which the signals must travel (e÷g., generally 600-10,000 kilometers). Forward Error Correction (FEC) is a technique used to help compensate for this distortion and provide "margin improvements" to the system. The margin improvements can be used to increase amplifier spacing or increase system capacity, h a Wavelength Division Multiplexing (WDM) system, the margin improvement can be used to increase the bit rate of each WDM channel, or decrease the spacing between WDM channels thereby allowing more channels for a given amplifier bandwidth. Accordingly, improvements in FEC techniques directly translate into increased capacity for long-haul communication systems. FEC coding is essentially the incorporation of a suitable code into a data stream for the detection and correction of data errors about which there is no previously known information. Error correcting codes are generated for a stream of data (i.e., encoding) and are sent to a receiver. The receiver recovers the error correcting codes and uses them to correct any errors in the received stream of data (i.e., decoding). An important property of deterministic codes is that they can uniquely decode any errors in the data and consequently correct them, within certain constraints. The challenge is to find "suitable" codes that can be efficient in terms of both complexity and cost for a given system. There are a large number of error-correction codes, each with different properties that are related to how the codes are generated and consequently how they perform. Some examples of these are the linear and cyclic Hamming codes, the cyclic Bose-Chaudhuri-Hocquenghem (BCH) codes, the convolutional (Viterbi) codes, the cyclic Golay and Fire codes, and some newer codes such as the Turbo convolutional and product codes (TCC, TPC). The codes that are frequently used for application in high bit-rate communication systems, however, are a set of cyclic, non-binary, block codes known as Reed-Solomon (RS) codes.

Conventional long-haul communication systems typically use the "RS 255/239" error-correction code to perform FEC. The RS 255/239 error-correction code yields approximately 5 decibels (dB) coding gain with about 6.7% redundancy. Due to various engineering margins, beginning-of-life (BOL) Q of these FEC-enhanced systems is on the order of 15 dB. This permits the design of systems with end-of-life (EOL) Q as small as 11.2 dB. The term "Q" refers to one measure of the signal-to-noise ratio (SNR) of a system. Since nonlinear impairments are still the prevailing limitation of system capacity, a greater coding gain above that provided by RS 255/239 would allow for further capacity improvements. There are coding techniques that provide higher coding gains of 10 dB or higher. These coding techniques, however, need more than 100% signal redundancy and therefore higher line rates. Current long-haul communication systems are limited to line rates of approximately 12.5 Gbps, and therefore cannot take advantage of these coding techniques without sacrificing capacity. Furthermore, these coding techniques require a soft decision receiver that increases latency and costs for the system.

In view of the foregoing, it can be appreciated that a substantial need exists for an enhanced FEC method and apparatus that solves the above-discussed drawbacks and deficiencies.

SUMMARY OF THE INVENTION

One embodiment of the invention comprises a method and apparatus to perform error correction. A stream of data is encoded using concatenated error correcting codes. The encoded data is communicated over a long-haul transmission system. The encoded data is decoded using the codes.

With these and other advantages and features of the invention that will become hereinafter apparent, the nature of the invention may be more clearly understood by reference to the following detailed description of the invention, the appended claims and to the several drawings attached herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a system suitable for practicing one embodiment of the invention.

FIG. 2 is a block diagram of a FEC encoder in accordance with one embodiment of the invention.

FIG. 3 is a block diagram of a FEC decoder in accordance with one embodiment of the invention.

FIG. 4 is a block flow diagram of the operations performed by an FEC codec in accordance with one embodiment of the invention.

FIG. 5 is a block flow diagram of an encoding process in accordance with one embodiment of the invention. FIG. 6 is a block flow diagram of a decoding process in accordance with one embodiment of the invention. FIG. 7 is an illustration of packing code blocks into a frame in accordance with one embodiment of the invention.

FIG. 8 is an illustration of the interleaving process in accordance with one embodiment of the invention. FIG. 9 illustrates plots of the theoretical upper bounds showing BER versus

Q in accordance with one embodiment of the invention.

FIG. 10 illustrates a first set of plots of a theoretical error bound in accordance with one embodiment of the invention.

FIG. 11 illustrates a second set of plots of a theoretical error bound in accordance with one embodiment of the invention.

FIG. 12 illustrates a plot of simulation results against the theoretical error bound in accordance with one embodiment of the invention.

FIG. 13 illustrates a plot comparing coding gains from various concatenated RS codes in accordance with one embodiment of the invention. FIG. 14 illustrates a plot of interleave depth versus coding gain in accordance with one embodiment of the invention.

DETAILED DESCRIPTION

The embodiments of the invention include a method and apparatus to increase coding gains in a long-haul communications system using concatenated error-correcting codes ("concatenated codes" or "product codes"). A long-haul communications system is defined herein to include any system designed to transport signals over a distance of greater than 600 kilometers. For example, a long-haul optically amplified undersea communication system is typically engineered to carry signals from one continent to another (e.g., North America to Europe). Concatenated codes refer to the use of two or more levels of FEC coding. The performance improvement from concatenated codes arises from the fact that any residual errors from one level of decoding will be corrected in the second level of decoding.

Concatenated codes are designed to have a strong first-level (inner) code (e.g. t = 16) followed by a weaker second-level (outer) code (e.g. t = 8), with an interleaving step in between the two. Interleaving re-distributes or "spreads" the errors from an undecodable inner code block over several outer code blocks. The re-distribution or spreading of errors brings the average number of errors per code block to within the error-correction capability of the code at least at the outer decoding level. The interleaver provides an FEC coding improvement corresponding to the depth of interleaving ("interleave depth") as discussed below.

One embodiment of the invention utilizes RS error correcting codes. An

RS code word consists of a "block" of n "symbols", k of which represent the data, with the remaining (n - k) symbols representing the redundancy or check symbols. These check symbols are appended to the data symbols during the encoding step, and are used to uniquely detect and correct bit errors at the decoder, within the error-correction capability of the code. After the decoding operation, the check symbols are stripped from the block, and the corrected data symbols are obtained. The data symbols themselves are left unmodified during the encoding step, and it is for this reason that the RS code is referred to as a "systematic" code. The rate of the RS code is the ratio of data symbols (or equivalently, bits) to code-word symbols (or bits). The overhead of the code is the ratio of the check symbols to code-word symbols, i.e., the overhead = ((1/rate) - 1).

The non-binary nature of block RS codes is manifest in the fact that a code symbol is not exactly a bit but rather it consists of several bits. The typical symbol size m is 8 bits, or a standard byte. The number of check symbols used determines the error-correction capability of a particular RS code. For example, a code that can correct t symbol errors in a block of n symbols requires at least 2t check symbols, so that the number of data symbols that can be transmitted in this block is k = n - 2t. Furthermore, for a given symbol size m, the maximum number of symbols per block, n, has to be less than or equal to 2^m - 1 to ensure unique decodability. For example, for m = 8, we have n = 255, and for t = 8 symbol errors in this case, the maximum number of data symbols is k = 239. This is represented in compact form as a 255/239 (n/k) RS code. RS error correcting schemes also include the use of a shortened RS code.

A shortened RS code is one where some of the data symbols are left unused. For example, a shortened 223/207 RS code of length n* = (n - s) = 223 symbols transmits 207 data symbols, in a block with error correction capability of up to 8 symbol errors. The disadvantage of shortened codes, relative to full-length codes, is that they are rate-inefficient. Some practical considerations, such as the maximum number of code-word symbols having to be n* ( < ) in some cases, however, may actually require this form. Shortened codes are implemented in both software and hardware by transforming a (n - s)/(k - s) RS code to a nlk code by padding s dummy symbols (e.g. 0) before encoding. At the decoder, this operation is reversed. After decoding, the padded symbols are stripped from the block.

A desirable property of RS codes is that they are maximum-distance codes. This means that there is sufficient uniqueness between code words such that the maximum number of errors in the (encoded) message can be corrected, for a given amount of redundancy, without the occurrence of a decoding error. This directly reflects the efficiency of these codes.

The decodability of the RS code can be demonstrated with a brief example. If the bit-error rates (BER) of the transmission channel is such that only a single symbol error is expected (t = 1), 2t check symbols are required. In the case of an 8-bit symbol (m = 8), this translates to 16 check bits. Of the 16 bits in this code, 8 bits are used to uniquely locate the symbol error (one out of 2 = 256 possibilities, corresponding to one out of 255 symbol positions, in addition to the error-free case). The remaining 8 bits are used to uniquely determine the error pattern (one out 2 = 256 error patterns, including the error-free pattern). Various procedures for encoding and decoding RS code words are well-known in the art, and therefore will not be further described herein.

The use of concatenated codes provides relatively powerful error correction with relatively little additional processing power. The overhead of a 2-level concatenated RS code can be calculated as

- 1, where ri and r₂ are the rates of the inner and outer codes, respectively. The concatenated RS code itself can be represented in compact form as rc₂/fc₂ -

where the subscripts 1 and 2 represent the inner and outer codes, respectively. Conventional FEC coding schemes (e.g., RS 255/239) provide a transmission performance improvement equivalent to a Q- f actor of about 5 dB while providing 7% extra bits as redundancy. One embodiment of the invention uses a concatenated RS code that provides an additional coding gain of approximately 2 dB while providing and extra 16% redundancy bits (a total of 23%). The embodiment uses an FEC encoder/decoder using a concatenated RS coding scheme with interleaving between the stages. More particularly, the FEC encoder/decoder utilizes a concatenated RS code of 223/207-255/223.

Since line rates are currently technically limited to 12.5 Gbps, concatenated rate-efficient block codes were examined assuming a linear-channel model with additive white Gaussian noise (AWGN). Under this assumption, concatenated block codes are available that perform at rates from 0.80 to 0.8333 (i.e., signal redundancy between 25 and 20%) and net coding gains somewhere between 1.5 dB to 2.5 dB greater than the gain achieved with the conventional RS 255/239 code.

At least two important discoveries were significant in implementing concatenated codes in long-haul communication systems. The first was the recognition that concatenated codes having an inner code that is stronger (i.e., lower code rate) than the outer code (i.e., higher code rate) is particularly useful in such systems. The second was the recognition that the class of codes utilized for the concatenated code significantly impacted system design.

With respect to the second discovery, two types of combinations were considered particularly advantageous for long-haul communication systems. The first combination comprised a bit-based BCH inner code and a byte-based BCH outer code (referred to herein as "BCH-RS concatenated code"). This is because bit-based BCH codes are good for more uniformly distributed errors while RS codes are good for "bursty" channels. When an inner decoder cannot correct all the errors on the line, it starts generating bursts that can then be effectively handled by the outer RS decoder. The second combination comprised a pair of RS codes (referred to herein as "RS-RS concatenated code"). RS codes having a range from t = 2 to t = 16 were examined, with t representing a code strength that is defined as the maximal possible number of corrected symbols per code word. The examination revealed that the concatenation of two RS codes of different strength would be particularly effective for undersea systems, provided that the outer code is interleaved before it is concatenated with the inner code. Interleaving is a technique that is normally used to spread bursty errors among several consecutive code words. In this case an interleaver is inserted between the two concatenated codecs so that the inner and the outer decoding processes are statistically de- correlated. In general practice, the greater the interleave depth the better coding performance is gained. The BCH-RS concatenated code and the RS-RS concatenated code each offers advantages according to the needs and constraints of a particular system. For example, the BCH-RS concatenation is good for channels that are both uniform and bursty in nature. The RS-RS concatenation is particularly good for bursty environments. Consequently, the RS-RS concatenation is well-suited to undersea communications systems since undersea channels are more bursty in nature.

Another important aspect of implementing an enhanced FEC system concerns digital frame alignment and synchronization in a very noisy environment. This is an important implementation issue because the enhanced FEC must operate at BER values as high as 5xl0^"2. The framing and synchronization strategies used in conventional FEC systems are inadequate for conditions where BER is greater than 10^"4.

It is worthy to note that any reference in the specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment.

Referring now in detail to the drawings wherein like parts are designated by like reference numerals throughout, there is illustrated in FIG. 1 a system suitable for practicing one embodiment of the invention. FIG. 1 is a block diagram of a long-haul communications network 100 comprising a communications transmitter/receiver ("transceiver") 102 and a transceiver 108 connected via a network 106. Transceivers 102 and 108 each include a FEC encoder/decoder ("FEC codec") 104 and a FEC codec 110, respectively. In this embodiment of the invention, long-haul communications network 100 is a conventional long-haul optically amplified undersea communication system with the optical transceivers modified to operate with a novel FEC codec performing in accordance with a novel concatenated FEC coding scheme. Network 100 in general, and network 106 in particular, are designed to transport optical signals over distances greater than 600 kilometers. FIG. 2 is a block diagram of a FEC encoder in accordance with one embodiment of the invention. FIG. 2 illustrates a FEC encoder 200 representative of the structure performing the concatenated encoding function of FEC codecs 104 and or 110. FEC encoder 200 comprises a first encoder 204, an interleaver 206 and a second encoder 208. First encoder 204 is also referred to herein as an "outer encoder." Second encoder 208 is also referred to herein as an "inner encoder." The operation of FEC encoder 200 will be discussed in more detail below with reference to FIGS. 4-6 and accompanying examples.

FIG. 3 is a block diagram of a FEC decoder in accordance with one embodiment of the invention. FIG. 3 illustrates a FEC decoder 300 representative of the structure performing the concatenated decoding function of FEC codecs 104⁽ and/or 110. FEC decoder 300 comprises a first decoder 304, a deinterleaver 306 and a second decoder 308. First decoder 304 is also referred to herein as an "inner decoder." Second decoder 308 is also referred to herein as an "outer decoder." The operation of FEC decoder 300 will also be discussed in more detail below with reference to FIGS. 4-6 and accompanying examples.

For purposes of clarity, the encoding structure and functionality (i.e., FEC encoder 200) is discussed separately from the decoding structure and functionality (i.e., FEC decoder 300). It can be appreciated, however, that both the encoding and decoding structure and functionality can be combined into a single FEC codec (e.g., FEC codecs 104 and 110) and still fall within the scope of the invention.

The operation of systems 100, 200 and 300 will be described in more detail with reference to FIGS. 4-6. Although FIGS. 4-6 presented herein include a particular sequence of steps, it can be appreciated that the sequence of steps merely provides an example of how the general functionality described herein can be implemented. Further, each sequence of steps does not have to be executed in the order presented unless otherwise indicated. FIG. 4 is a block flow diagram of the operations performed by an FEC encoder in. accordance with one embodiment of the invention. In this embodiment of the invention, FEC encoder 202 performs the FEC encoding. FIG. 4 illustrates a FEC process 400. A stream of data is encoded using concatenated error correcting codes at step 402. The encoded data is communicated over a long-haul transmissions system at step 404. In one embodiment of the invention the long- haul transmission system communicates the encoded data at least 600 kilometers. The encoded data is decoded using the error correcting codes at step 406.

FIG. 5 is a block flow diagram of an encoding process in accordance with one embodiment of the invention. FIG. 5 illustrates an encoding process 500 that is representative of step 402 described with reference to FIG. 4. The stream of data is packed into a first frame of first blocks at step 502. The first frame is also referred to herein as an "unencoded outer frame." A first error correcting code is generated for each of the first blocks at step 504. The first error correcting codes are appended to the first blocks to create a second frame of second blocks at step 506. The second frame is also referred to herein as an "encoded inner frame." The second frame of second blocks is packed into a third frame of third blocks at step 508. The third frame is also referred to herein as an "unencoded inner frame." A second error correcting code is generated for each of the third blocks at step 510. The second error correcting codes are appended to the third blocks to create a fourth frame of fourth blocks at step 512. The fourth frame is also referred to herein as an "encoded outer frame."

The first frame, second frame, third frame and fourth frame each have a predetermined length. In one embodiment of the invention, the length of the second frame matches the length of the third frame. In this manner, no padding is required for the third frame. This decreases the latency associated with such padding hardware and techniques. In alternative embodiments, however, the length of the second frame is less than the length of said third frame. In such a case, the third frame is padded with padding symbols until the length of the third frame matches the length of the second frame. In this case, the increase in FEC coding efficiency is sufficient to compensate for the latency incurred by padding. The embodiments of the invention use interleaving during the encoding and decoding process. More particularly, the interleaving operation occurs during the packing of the second blocks from the second frame into the third blocks of the third frame, and vice-versa. It can be appreciated, however, that the interleaving process can occur as a separate step from the packing process and still fall within the scope of the invention. The interleaving operation can be either bit interleaving or byte interleaving. In one embodiment of the invention, the third frame has a number 1-N of third blocks, with N matching an interleave depth for the encoding process. In one advantageous embodiment N = 64, while in another N =16. The error correcting codes can be any code from a group comprising the linear and cyclic Hamming codes, the cyclic BCH codes, the convolutional Viterbi codes, the cyclic Golay and Fire codes, and some newer codes such as TCC and TPC. The concatenated error correcting code pair may be separately represented as a first and second error correcting code, with the first error correcting code represented as x/y, and the second error correcting code represented as z/x. In one embodiment of the invention, the first error correcting code is a reed-solomon code. More particularly, the first error correcting code is a xl207 reed-solomon error correcting code. The second error correcting code is also a reed-solomon code. The second error correcting code is a 255/x reed-solomon error correcting code. In one advantageous embodiment of the invention, the x is equal to 223 symbols. This two level FEC coding results in a net coding gain of approximately 1.8 decibels while performing at a bit error rate of 10^"10. This embodiment adds a redundancy percentage to the communicated encoded data of approximately 23 percent. In an alternative embodiment of the invention, the first error correcting code is one of a group comprising a bit based BCH code and a byte based BCH code. The second error correcting is also one of a group comprising a bit based BCH code and a byte based BCH code. Further, the first error correcting code is stronger than the second error correcting code. FIG. 6 is a block flow diagram of a decoding process in accordance with one embodiment of the invention. FIG. 6 illustrates a decoding process 600. The second error correcting codes and third blocks are recovered from the fourth blocks at step 602. The second error correcting codes are used to correct errors for the third blocks at step 604. The second blocks are unpacked from the third blocks at step 606. The unpacking process also includes a deinterleaving operation described below. The first error correcting codes and the first blocks are recovered from the second blocks at step 608. The first error correcting codes are used to correct errors for the first blocks at step 610.

The operation of systems 100, 200 and 300, and the flow diagram shown in FIGS. 4-6, can be better understood by way of example. A software-based Monte- Carlo simulation was developed in C for fast processing of the encoding and decoding operations. As described above, the concatenated RS codes involve two independent levels of RS encoding (and decoding), with an interleaving (de- interleaving) step in between them.

FIG. 7 is an illustration of how code blocks are packed into a frame in the encoding step. An integral number of first blocks 702 at the first (outer) encoding level are packed into a first frame 704 (i.e., the unencoded outer frame). Check symbols 706 for first blocks 702 are generated by a first encoder (e.g., first encoder 204) of a FEC encoder (e.g., FEC codec 104 or FEC encoder 200). Check symbols 706 are appended to first blocks 702 to form second blocks 708. Second blocks 708 are packed into a second frame 710 (i.e., the encoded outer frame). The bits (or bytes) from second blocks 708 are interleaved, and they are packed into third blocks 714 of a third frame 712 (i.e., unencoded inner frame). In this example, second frame 710 and third frame 712 have the same length in terms of bits (or bytes), although the block size will likely vary between the two frames. In other words, third frame 712 is required to be an integral number of third blocks 714, the size of which is different from that of second blocks 708. Thus, in order for second frame 710 and third frame 712 to be of the same length, the number of second blocks 708 and third blocks 714 per frame in each of these frames, respectively, has to be chosen appropriately.

If second frame 710 and third frame 712 cannot be made to match with an integral number of blocks, third frame 712 is padded or "stuffed" with dummy symbols until they are of equal length. The padding process, however, represents an increase in latency in a hardware implementation, or increased processing time in software, i one embodiment of the invention, the lengths of the frames are therefore chosen to minimize the number (or reduce to zero) of stuffed symbols, while at the same time keeping the number of second blocks per second frame to a minimum. Once second blocks 708 from second frame 710 are packed and interleaved into third blocks 714 of third frame 712, check symbols 716 are generated for third blocks 714 by a second encoder (e.g., second encoder 208) of an FEC encoder (e.g., FEC codec 104 or FEC encoder 200). Check symbols 716 are appended to third blocks 714 to form a set of fourth blocks 718 of a fourth frame 720 (i.e., the encoded inner frame). Once the two-level encoding process is performed, the encoded data stream is communicated to a transceiver (e.g., transciever 108) for decoding by a FEC decoder (e.g., FEC codec 110 or FEC decoder 300).

FIG. 8 is an illustration of the interleaving process in accordance with one embodiment of the invention. As shown in FIG. 8, interleaving between the two encoding steps discussed with reference to FIG. 7 (between packing the second and third frames) amounts to re-distributing the errors in bit-groupings or bytes that are either 1-bit or 8-bits long. FIG. 8 illustrates an example of byte interleaving after second frame 710 is encoded. The improvement in error correction is directly related to the depth of interleaving. Using the example illustrated in FIG. 8, full byte (or symbol) interleaving requires that each of the 223 symbols in each second block 708 (i.e., the outer frame) is re-distributed into 223 different third blocks 714 (i.e., the inner frame). In the case of full interleaving, the 223 symbols would require an interleave depth of 223 levels or 223 third blocks 714. If full bit interleaving were required in this case, each of the 223 x 8 bits in each of second blocks 708 would be re-distributed into 223 x 8 = 1784 different third blocks 714. In this case, the interleave depth is 1784 levels. Although full bit or byte interleaving improves the error correction, the disadvantage of full interleaving is the large amount of memory required and the additional latency in a practical implementation. Prior to evaluating the results of the software-based Monte-Carlo simulation described above, theoretical BER error bounds were established to provide a basis for comparison. The theoretical BER error bounds estimate the maximum BER that is observed after error correction, using a particular code, of a message transmitted through a channel with a specific line BER. This served as a benchmark to ensure that both software-based and hardware-based codes were performing "correctly." The benchmark also served as a way to efficiently evaluate and compare the performance of several different codes. The theoretical error bound was established using the following assumptions:

1. A binomial distribution of un-correlated bit errors is observed on the channel (note that for BER < 10^_1, the Binomial distribution can be approximated by a Poisson distribution, and for a large number of events, or transmitted bits, the Binomial probability distribution can be approximated by a normal distribution under certain conditions that are valid in this case);

2. No additional errors are committed at the decoder if it is found that a block is undecodable because the errors are passed through unchanged;

3. Errors are equally likely to occur in the data and check symbols so that number of residual errors is reduced further when check symbols are stripped from the block; and

4. For BER < 5 x 10 ² at most 2 bit errors per symbol error are likely to occur.

FIG. 9 illustrates plots of the theoretical upper bounds showing BER versus Q in accordance with one embodiment of the invention. The comparison with conventional error bounds indicates the estimate of the BER after error correction (1) follows the line or channel BER very closely when the error-correction capability is exceeded when the line BER is ~ 10^-2, and (2) is a less-conservative estimate of the maximum estimated BER after correction. The "looser" upper bound was subsequently justified by strong agreement with the results from the software-based Monte-Carlo simulation of the BER.

FIG. 10 illustrates a first set of plots of a theoretical error bound in accordance with one embodiment of the invention. The theoretical model was verified by evaluating the theoretical performance of single-level RS codes. For example, the use of 7% RS (FEC) codes yield a coding gain in Q of greater than 5 dB at an output BER level of 10^~10 over unencoded transmission. The legend in FIG. 10 also reflects a δQ reduction in the coding gain due to transmission at higher bit rates. The distinction between gross and net coding gain in Q is discussed with reference to FIG. 11.

FIG. 11 illustrates a second set of plots of a theoretical error bound in accordance with one embodiment of the invention. The Q of the system is defined as usual, and any increase in Q due to error-correction coding is defined as coding gain. There is a difference, however, between a "gross gain" and a "net gain" in Q. More particularly, the gross gain does not account for the system impairment from the increased noise bandwidth, and consequent reduction in Q, due to transmission at higher line rates. The transmission performance plots shown in FIG. 11 thus indicate the gross coding gain, through a direct conversion from the BER after error correction to the system Q in dB. The loss in Q, however, is reflected separately in the plots (in the legend), where δQ represents an adjustment to the coding gain as a function of the modified (higher) line rate due to the overhead - this then gives the net coding gain. This is shown to provide an estimate of the net gain that will be computed in an actual wet-system simulation that accounts for various system impairments such as nonlinearity in the fiber, inter-symbol interference, chromatic dispersion, and so forth.

FIG. 12 illustrates a plot of the simulation results against the theoretical error bound in accordance with one embodiment of the invention. As shown in FIG. 12, results of the simulation, for BER after error correction, compared extremely favorably to the theoretical error bounds. The agreement was good for single-level RS codes, concatenated RS codes, and concatenated, shortened RS codes. Furthermore, two separate C programs were independently developed, one for the Monte-Carlo simulation, and another for incorporation into a system experiment, where the encoding, decoding, interleaving, de-interleaving, frame and PRBS-pattern synchronization, were software-based. The two programs yielded almost identical results for the BER improvement after error correction, confirming not only the correct implementation of the various algorithms, but also the robustness of the frame synchronization.

In one embodiment of the Monte-Carlo simulation, the speed of the C-code is about 464 blocks per second of decoding on a 350 Megahertz (MHz), Pentium-II processor with 64 Megabytes (MB) of Random Access Memory (RAM). A single, random, encoded frame is re-sent several times through the channel until an encoded bit- stream of sufficient length is transmitted. The random noise introduced to each frame, however, is different as the computer's system clock is used to generate a seed for the (C) random-number generator (e.g., "srand").

FIG. 13 illustrates a plot comparing coding gains from various concatenated RS codes in accordance with one embodiment of the invention. Several RS codes were evaluated with symbol size of 8 bits because this is the most common hardware implementation for RS coding. This translates to a full code-block length of 255 symbols, each 8 bits long. Furthermore, overhead was constrained to a maximum of 23% since next generation terminal designs are limited to line rates of approximately 12.3 - 12.5 Gbps. Consequently, a set of concatenated RS codes having a net overhead (inner and outer codes) fixed at 23% (i.e. t_\ + t₂ = to, where t_\ and t₂ are the number of symbol errors that can be corrected in the inner and outer codes, and their sum, which is the net error correction capability) were examined. FIG. 14 illustrates a plot of interleave depth versus coding gain in accordance with one embodiment of the invention. The effect of the depth of primarily bit and (8 -bit) byte interleaving provides varying results in terms of coding gain for the system. As shown in FIG. 13, deeper levels of byte interleaving (e.g., up to 223 levels for a 223/207-255/203 code) improve coding performance but with marginal gains beyond about 64 levels of byte interleaving. This is significant since deeper levels of interleaving utilize more memory and increase latency without providing much coding gain. The loss in coding from byte-interleaving from 64 to 16 levels is about 0.27 dB at output BER levels of lo-⁹.

Byte interleaving yields better error-correction than bit-interleaving. This is because 1-2 bit-errors per symbol error at line BER of 10^-2 and smaller on average is demonstrated. This means that symbol (or byte) interleaving is desirable to spread out the residual bit errors from the first level of decoding (inner decoding). Bit-interleaving on the other hand may not re-distribute the residual bit errors "maximally" unless full bit interleaving is implemented (223 x 8 levels). The disadvantage in this implementation then is that additional software processing time or hardware latency is required.

The net coding gain for the 223/207-255/223 concatenated RS code was evaluated. The reason that this particular combination was singled out is that its inner and outer code block lengths are such that they can be efficiently packed into a frame that can be as short as one unencoded inner block, with k_\ = 223 (or equivalently, one encoded outer block, with n₂ = 223). Furthermore, this mode corrects up to 16 symbol errors in the inner code, and up to 8 symbol errors in the outer one - this is compatible with existing core encoder/ decoder designs from LSI Logic which supports coding engines that can correct anywhere from 3 to 16 symbol errors in a block that is up to 255 symbols long. The net coding for this code at output BER of 10^-10 is estimated to be 1.8 dB, relative to the 7%-overhead RS 255/239 FEC code, as illustrated in Table 1.

Table 1

RS concatenated code 215/207-255/215 was also considered since it provides better error-correction with the same overhead. This represents a stronger inner code which corrects up to 20 symbols errors, and a weaker outer code which corrects up to 4 symbol errors. Modifying the hardware design for t = 20 by LSI Logic and ASIC International is possible to implement this type of code. The net coding gain for this code at output BER of 10^-10 is about 2 dB, relative to the 7%- overhead RS 255/239 FEC code (see Table 1). Other RS codes with symbol sizes other than 8 bits (e.g., 9 and 7 bit-long symbols) are possible, but may require modifications to existing core designs for the encoder and decoder.

The RS codes considered herein are rate-efficient codes with good error- correction performance in high bit-rate communication systems. The complexity of the encoding and decoding operations is also not too high so that a hardware implementation is both feasible and cost-effective. The constraint on the maximum overhead allowed for error correction (about 23%) is imposed by terminal hardware speeds. This limits systems, in one embodiment of the invention, to concatenated RS codes of the form x/207 - 255 x, where x is a measure of the asymmetry of the strengths of the inner and outer codes. One embodiment of the invention includes x to be 223 because this is a good performing code based on existing core hardware designs for the encoder and decoder. The net coding gain for this code at an output BER of 10^~10 is estimated to be about 1.8 dB, relative to the 7%-overhead RS 255/239 FEC code.

Byte interleaving appears to be marginally better than bit-interleaving in terms of performance, but may have a greater impact on hardware designs in terms of reduced latency and a smaller memory requirement. The depth of byte interleaving can be limited to about 64 levels, and even to as few as 16 levels, without sacrificing much coding gain. This may have significant impact on the architecture of the hardware in that up to 16 parallel coding engines can be accommodated on a single chip currently. The core designs for the coding engine can be modified to support RS codes that can correct up to 20 symbol errors per block, or RS codes with symbol sizes of 9 and 7 bits. Consequently, other promising codes that offer additional coding gain are available. Other potential code types include a 3-level concatenated RS code, and a 2-level concatenated RS code that are further concatenated with bit-based codes such as BCH codes. These offer further improvement ^• in error correction, with the disadvantage being "diminishing returns" on additional levels of coding, and increased latency. Finally, a class of codes known as Turbo codes provides superior performance as well.

Factors that may affect implementation of enhanced FEC coding as described herein include the effects of chromatic dispersion, Kerr non-linearity, and polarization fading. These effects will cause the noise properties of a communication channel to be different from the computer simulations and theory used above. The assumption used above is that the noise is AWGN causing binomially-distributed errors. A testing platform can test EFEC over a real, long distance, optical channel.

The test platform will test various EFEC codes by encoding and decoding in software. The optical channel is implemented by looping a short span of amplifiers (200-500 km) using standard techniques. The encoded data is generated by a computer program and loaded into a Bit Error Rate Test Set (BERTS) (8 Mb). After transmission through the loop, every sixteenth bit of the noisy data is acquired by a high-speed data acquisition unit. This data is stored on a hard disk or removable disk for subsequent data processing. Well-generalized computer programs can generate properly encoded and framed data, as well as decoding the acquired data. These programs are capable of:

• Different Code Types: concatenated RS, BCH, and eventually Turbo codes

• Reed-Solomon Codes with variable block length ( ), overhead (n - k) and symbol size ( )

• Frame Alignment: user-specified Frame Alignment Word (FAW)

• PRBS generation and re-synchronization with variable word length

• Interleaving: variable bit groupings (e.g., bit and byte interleaving) and variable number of blocks per frame

• Burst boundary detection and re-synchronization

• Error detection: i.e., the software acts as the receiving BERTS

• Roll control: independently determine the roll state for each burst of data from the loop

• Interleaving of 16 valid data streams for the transmitter

• Interface to the BERTS .

An example of FEC 104, FEC 110, FEC encoder 202 and FEC decoder 302, includes a modified RS code engine made by LSI Logic. These engines were developed for "100 K" LSI 0.8 micrometer Complementary Metal-Oxide Semiconductor (CMOS) process. The t = 8 engine is also applied in conventional FEC Application Specific Integrated Circuits (ASICs). LSI Logic has since introduced three newer CMOS processes G10, Gil and G12. G12 process is the newest 0.18 micrometer geometry standard cell array with supply voltage options of 1.5 V, 2.5 V and 3.3 V depending on processing speed. This particular process allows for integration on several million logic cells with high speed processing cores. It is anticipated that the G-12 serial processing speed could be greater than 1 Gbps and the interfaces could be made as fast 2.5 Gbps. This would be sufficient to meet the requirements of at least one embodiment of the invention, which are input/output (I/O) interface speed of less than 780 Mbps and processing speed less than 390 Mbps. Since a large part of the processor logic circuit will operate at much lower speed, a majority of the cells could be powered with the low- voltage (1.8 V) option. Consequently, the power dissipation could be significantly reduced in comparison with the latest 2.5 Gbps FEC design on the G10 process. Accordingly, at least one embodiment of the invention can be implemented utilizing the enhanced FEC 12.5 Gbps codec unit with two to four G12 ASICs that will include the framing logic, buffers, most of the timing functions, the overhead multiplex and processing. This would also include a rather deep interleaver, which is needed for de-correlation of the two concatenated coding processes. The compilers exist between 100 kilobytes (K) and G12 process which are suitable for one embodiment of the invention. Consequently, core engine implementation can be implemented through modification of the compiler. Further, the production cost could be markedly reduced and the reliability considerably improved through the capability of an ultra large scale of integration. Other potential FEC codecs with similar or better performance than LSI

Logic G-12 process include those designed by Motorola, Texas Instruments, IBM, and so forth. Although these technologies could not use the LSI Logic core designs, other RS and BCH core designs are available and are just as robust. In particular, AHA Inc. makes a wide spectrum of RS core designs with an option of erasure that would make a concatenated code more efficient.

In addition, it can be appreciated that RS and BCH core designs are available for implementation on programmable logic arrays (PLA). These are referred to as the "Hammer Codes." PLA implementation of additional coding of the overhead bytes (bits), external to the high-speed payload codec, would be very useful.

The feasibility of frame alignment and framing at very high BER rate (BER > 10^"2) for 10 Gbps payloads have also been evaluated. The evaluation reveals that a number of different frames are possible. It appears, however, that shorter frames are more robust than longer frames. Further, it would be beneficial if the FAW and the associated overhead bits (OW and dedicated data channels) are not coded with the payload. Rather, they should be coded separately at much lower speed and possibly at a lower code rate since there would be plenty of redundant bits available in a practical frame.

Optimal frame alignment methods and de-synchronization strategies have been explored. The studies indicate that the optimal FAW length is 16 bits, and that RS decoder engine "error diagnostics" should be used to start a frame re- alignment process.

The testing of hardware core designs would also be beneficial in addition to the software approach of undersea channel coding tests described above. Low speed integrated circuits (ICs) for LSI Logic RS and BCS core designs are available. In addition, a low speed IC for an AHA RS codec is also available. Potential test candidates include technology developed by Lockheed Martin Satellite division (previously Mount Whitney), which owns BCH and RS core designs on Vitesse Gallium Arsenide (GaAs) gate arrays. The processing speed for these codecs is approximately 620 Mbps.

All these "codec ICs" are programmable, and need external frame alignment, First-In First-Out (FIFOs), and timing circuits. This calls for a set of test boards. They should be developed to test ASIC prototypes to avoid problems in later implementation. The hardware testing boards are useful for system tests, both before and during the ASIC design phase. An initial design of low and highspeed test boards for LSI Logic ICs that will be able to test concatenated RS schemes has already been established.

Although various embodiments are specifically illustrated and described herein, it will be appreciated that modifications and variations of the present invention are covered by the above teachings and within the purview of the appended claims without departing from the spirit and intended scope of the invention. For example, although the embodiments of the invention discuss a particular concatenated RS codec at the given signal redundancy constraint (< 24%), it can be appreciated that additional coding gains may be achieved by concatenation of a RS and a punctured convolutional code, or concatenation of BCH and RS codes. The problem with punctured convolutional schemes is that a soft-decision receiver is required. The particular system design must take into consideration the difficulty of its implementation versus potentially superior performance (about 0.5 dB). Similarly, BCH core designs are not readily available and therefore may require additional implementation time. Another example of suitable concatenated codes for an embodiment of the invention includes TPC that could yield as much as 10 dB coding gain, relative to the unencoded data, at only 26% signal redundancy. In another example, it can be appreciated that the functionality described for the embodiments of the invention may be implemented in hardware, software, or a combination of hardware and software, using well- known signal processing techniques. If in software, a processor and machine- readable medium is required. The processor can be any type of processor capable of providing the speed and functionality required by the embodiments of the invention. For example, the processor could be a processor from the Pentium® family of processors made by Intel Corporation, or the family of processors made by Motorola. Machine-readable media include any media capable of storing instructions adapted to be executed by a processor. Some examples of such media include, but are not limited to, read-only memory (ROM), random-access memory (RAM), programmable ROM, erasable programmable ROM, electronically erasable programmable ROM, dynamic RAM, magnetic disk (e.g., floppy disk and hard drive), optical disk (e.g., CD-ROM), and any other device that can store digital information. In one embodiment, the instructions are stored on the medium in a compressed and/or encrypted format. As used herein, the phrase "adapted to be executed by a processor" is meant to encompass instructions stored in a compressed and/or encrypted format, as well as instructions that have to be compiled or installed by an installer before being executed by the processor. Further, the processor and machine-readable medium may be part of a larger system that may contain various combinations of machine readable storage devices through various I/O controllers, which are accessible by the processor and which are capable of storing a combination of computer program instructions and data. Finally, in another example, the embodiments were described using a communication network. A communication network, however, can utilize an infinite number of network devices configured in an infinite number of ways. The communication network described herein is merely used by way of example, and is not meant to limit the scope of the invention.

Claims

CLAIMS:

1. A method to perform error correction, comprising: encoding a stream of data using concatenated error correcting codes; communicating said encoded data over a long-haul transmission system; and decoding said encoded data using said codes.

2. The method of claim 1, wherein said long-haul transmission system communicates said encoded data at least 600 kilometers.

3. The method of claim 1, wherein said encoding comprises: packing said stream of data into a first frame of first blocks; generating a first error correcting code for each of said first blocks; appending said first error correcting codes to said first blocks to create a second frame of second blocks; packing said second frame of second blocks into a third frame of third blocks; generating a second error correcting code for each of said third blocks; and appending said second error correcting codes to said third blocks to create a fourth frame of fourth blocks.

4. The method of claim 3, wherein each frame has a length.

5. The method of claim 4, wherein said length of said second frame matches said length of said third frame.

6. The method of claim 4, wherein said length of said second frame is less than said length of said third frame.

7. The method of claim 6, further comprising padding said third frame with padding symbols until said length of said third frame matches said length of said second frame.

8. The method of claim 3, wherein said packing said second frame of second blocks into a third frame of third blocks comprises interleaving said second blocks into said third blocks.

9. The method of claim 8, wherein said interleaving is bit interleaving.

10. The method of claim 8, wherein said interleaving is byte interleaving.

11. The method of claim 8, wherein said third frame has a number 1-N of third blocks, with N matching an interleave depth for said encoding.

12. The method of claim 9, wherein N is at most 64.

13. The method of claim 9, wherein N is 16.

14. The method of claim 3, wherein said first error correcting code is represented as x/y, and said second error correcting code is represented as z/x.

15. The method of claim 3, wherein said first and second error correcting codes are reed-solomon codes.

16. The method of claim 15, wherein said first error correcting code is a JC/207 reed-solomon error correcting code.

17. The method of claim 16, wherein said second error correcting code is a 255 x reed-solomon error correcting code.

18. The method of claim 17, wherein x = 223.

19. The method of claim 1, wherein said communicating is performed at a bit error rate of 10^"10 with a net coding gain of approximately 1.8 decibels.

20. The method of claim 1, wherein said encoding adds a redundancy percentage to said communicated encoded data of approximately 23 percent.

21. The method of claim 3, wherein said first error correcting code is one of a group comprising block codes, linear and cyclic Hamming codes, cyclic Bose-Chaudhuri-Hacquenghem (BCH) codes, convolutional Viterbi codes, cyclic Golay and Fire codes, Turbo convolutional codes and Turbo product codes.

22. The method of claim 3, wherein said second error correcting code is one of a group comprising block codes, linear and cyclic Hamming codes, cyclic Bose-Chaudhuri-Hacquenghem (BCH) codes, convolutional Viterbi codes, cyclic Golay and Fire codes, Turbo convolutional codes and Turbo product codes.

23. The method of claim 3, wherein said first error correcting code is one of a group comprising a bit based Bose-Chaudhuri-Hacquenghem (BCH) code and a byte based BCH code.

24. The method of claim 3, wherein said second error correcting code is one of a group comprising a bit based Bose-Chaudhuri-Hacquenghem (BCH) code and a byte based BCH code.

25. The method of claim 3, wherein said first error correcting code is stronger than said second error correcting code.

26. The method of claim 1, wherein said decoding comprises: recovering said second error correcting codes and said third blocks from said fourth blocks; correcting errors for said third blocks using said second error correcting codes; unpacking said second blocks from said third blocks; recovering said first error correcting codes and said first blocks from said second blocks; and correcting errors for said first blocks using said first error correcting codes.

27. A machine-readable medium whose contents cause a computer system to perform error correction, comprising: encoding a stream of data using concatenated error correcting codes; communicating said encoded data over a long-haul transmission system; and decoding said encoded data using said codes.

28. The machine-readable medium of claim 27, wherein said long-haul transmission system communicates said encoded data at least 600 kilometers.

29. The machine-readable medium of claim 27, wherein said encoding comprises: packing said stream of data into a first frame of first blocks; generating a first error correcting code for each of said first blocks; appending said first error correcting codes to said first blocks to create a second frame of second blocks; packing said second frame of second blocks into a third frame of third blocks; generating a second error correcting code for each of said third blocks; and appending said second error correcting codes to said third blocks to create a fourth frame of fourth blocks.

30. The machine-readable medium of claim 29, wherein each frame has a length.

31. The machine-readable medium of claim 30, wherein said length of said second frame matches said length of said third frame.

32. The machine-readable medium of claim 30, wherein said length of said second frame is less than said length of said third frame.

33. The machine-readable medium of claim 32, further comprising padding said third frame with padding symbols until said length of said third frame matches said length of said second frame.

34. The machine-readable medium of claim 29, wherein said packing said second frame of second blocks into a third frame of third blocks comprises interleaving said second blocks into said third blocks.

35. The machine-readable medium of claim 34, wherein said interleaving is bit interleaving.

36. The machine-readable medium of claim 34, wherein said interleaving is byte interleaving.

37. The machine-readable medium of claim 34, wherein said third frame has a number 1-N of third blocks, with N matching an interleave depth for said encoding.

38. The machine-readable medium of claim 37, wherein N is at most 64.

39. The machine-readable medium of claim 37, wherein N is 16.

40. The machine-readable medium of claim 29, wherein said first error correcting code is represented as x/y, and said second error correcting code is represented as z/x.

41. The machine-readable medium of claim 29, wherein said first and second error correcting codes are reed-solomon codes.

42. The machine-readable medium of claim 41, wherein said first error correcting code is a x/207 reed-solomon error correcting code.

43. The machine-readable medium of claim 42, wherein said second error correcting code is a 255 x reed-solomon error correcting code.

44. The machine-readable medium of claim 43 , wherein x = 223.

45. The machine-readable medium of claim 27, wherein said communicating is ppeerfrfoorrmmeedd aatt aa bbiitt eerrrroorr rate of 10^'10 with a net coding gain of approximately 1.8 decibels.

46. The machine-readable medium of claim 27, wherein said encoding adds a redundancy percentage to said communicated encoded data of approximately 23 percent.

47. The machine-readable medium of claim 29, wherein said first error correcting code is one of a group comprising block codes, linear and cyclic

Hamming codes, cyclic Bose-Chaudhuri-Hacquenghem (BCH) codes, convolutional Viterbi codes, cyclic Golay and Fire codes, Turbo convolutional codes and Turbo product codes.

48. The machine-readable medium of claim 29, wherein said second error correcting code is one of a group comprising block codes, linear and cyclic Hamming codes, cyclic Bose-Chaudhuri-Hacquenghem (BCH) codes, convolutional Viterbi codes, cyclic Golay and Fire codes, Turbo convolutional codes and Turbo product codes.

49. The machine-readable medium of claim 29, wherein said first error correcting code is one of a group comprising a bit based Bose-Chaudhuri- Hacquenghem (BCH) code and a byte based BCH code.

50. The machine-readable medium of claim 29, wherein said second error correcting code is one of a group comprising a bit based Bose-Chaudhuri- Hacquenghem (BCH) code and a byte based BCH code.

51. The machine-readable medium of claim 29, wherein said first error correcting code is stronger than said second error correcting code.

52. The machine-readable medium of claim 29, wherein said decoding comprises: recovering said second error correcting codes and said third blocks from said fourth blocks; correcting errors for said third blocks using said second error correcting codes; unpacking said second blocks from said third blocks; recovering said first error correcting codes and said first blocks from said second blocks; and correcting errors for said first blocks using said first error correcting codes.

53. An apparatus to perform error correction, comprising: a forward error correction encoder to encode a stream of data using concatenated error correcting codes; and a transceiver connected to said encoder to communicate said encoded stream of data over a long-haul transmission system.

54. The apparatus of claim 53, wherein said encoder comprises: a first level encoder to encode said stream of data using a first error correcting code; an interleaver to interleave said first level encoded stream of data; and a second level encoder to encode said interleaved stream of data using a second error correcting code.

55. The apparatus of claim 54, wherein said first error correcting code and said second error correcting code are reed-solomon codes.

56. The apparatus of claim 55, wherein said first error correcting code is a x/207 reed-solomon error correcting code, and said second error correcting code is a 255/ reed-solomon error correcting code.

57. The apparatus of claim 56, wherein x = 223.

58. The apparatus of claim 57, wherein said transceiver communicates said encoded stream of data at a bit error rate of 10^"10 with a net coding gain of approximately 1.8 decibels.

59. The apparatus of claim 58, wherein said encoding adds a redundancy percentage to said communicated encoded stream of data of approximately

23 percent.

60. An apparatus to perform error correction, comprising: a transceiver to receive an encoded stream of data from a long-haul transmission system, wherein said encoded stream of data was encoded using concatenated error correcting codes; and a forward error correction decoder to decode said received stream of data using said concatenated error correcting codes.

61. The apparatus of claim 60, wherein said decoder comprises: a first level decoder to decode said received stream of data using a first error correcting code; a deinterleaver to deinterleave said first level decoded stream of data; and a second level decoder to decode said deinterleaved stream of data using a second error correcting code.

62. A system to perform error correction, comprising: a forward error correction encoder to encode a data stream using a concatenated code; a long-haul communication network to communicate said encoded data stream over a distance of 600 kilometers; and a forward error correction decoder to decode said encoded data stream using said concatenated code.